Amulti-dimensionally upwind conservative ResidualDistribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the ca...Amulti-dimensionally upwind conservative ResidualDistribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the case of the complex flowfield over a double cone configuration.The resulting numerical discretization combines a state-of-the-art nonlinear quasi-monotone second order blended scheme for distributing the convective residual and a standard Galerkin formulation for the diffusive residual.The physical source terms are upwinded together with the convective fluxes.Numerical results show an excellent agreement with experimental measurements and available literature.展开更多
We theoretically construct a rectangular phononic crystal(PC) structure surrounded by water with C2vsymmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex c...We theoretically construct a rectangular phononic crystal(PC) structure surrounded by water with C2vsymmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms:the vertical type, in which the distance s between the center of the scatterer and its right-angle point is greater than 0.5 a,and the transverse type, in which s is smaller than 0.5 a(where a is the crystal constant in the x direction). Each rectangular scatterer has three variables: length L, width D, and rotation angle θ around its centroid. We find that, when L and D change and θ is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary θ and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.展开更多
In order to investigate the damage characteristic of ceramic-metal interpenetrating phase composite（IPC） under dynamic loading, uniaxial dynamic compression was performed to characterize the failure of SiC/Al compos...In order to investigate the damage characteristic of ceramic-metal interpenetrating phase composite（IPC） under dynamic loading, uniaxial dynamic compression was performed to characterize the failure of SiC/Al composite with 15% porosity using a modifi ed Split Hopkinson Pressure Bar（SHPB）. High speed photography was used to capture the failure procedure and set up the relationship between deformation and real stress. The deformation control technology was used to obtain collected samples in different deformations under dynamic loading. Micro CT technology was utilized to acquire real damage distribution of these specimens. Moreover, SEM was employed in comparing the damage characteristics in IPC. A summary of the available experimental results showed that IPC without lateral confi nement formed double cones. The different features compared with ceramic materials without restraint was shown to be the result of the lateral restraint effect provided by metal phase to ceramics skeleton.展开更多
Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative ans...Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative answer to the question of Zhang.展开更多
The variable high-order multiblock overlapping(overset)grids method of Sj¨ogreen&Yee[CiCP,Vol.5,2009]for a perfect gas has been extended to nonequilibrium flows.This work makes use of the recently developed h...The variable high-order multiblock overlapping(overset)grids method of Sj¨ogreen&Yee[CiCP,Vol.5,2009]for a perfect gas has been extended to nonequilibrium flows.This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts[Wang et al.,J.Comput.Phys.,2009,2010]that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations.Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields,even under the multiblock grid or adaptive grid refinement framework.While low dissipative sixth-or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets,second-and thirdorder shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence.It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow for an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow.In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries.The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks,including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components,depending on the flow conditions.展开更多
We consider the boundary value problem for the second order quasilinear differential equationwhere f is allowed to change sign, φ(v) = \v\p-2v, p > 1. Using a new fixed point theorem in double cones, we show the e...We consider the boundary value problem for the second order quasilinear differential equationwhere f is allowed to change sign, φ(v) = \v\p-2v, p > 1. Using a new fixed point theorem in double cones, we show the existence of at least two positive solutions of the boundary value problem.展开更多
We study （pseudo-）differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are corner degenerate in ...We study （pseudo-）differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are corner degenerate in a specific way. They are described Cmodulo ＇lower order terms＇） by a principal symbolic hierarchy σ（A） = （σψ （A）, σ∧ CA）, σ∧ （A））, where σψ is the interior symbol and σ∧（A） （y, η）, （y, η） ∈ T＊Y／0, the Coperator-valued） edge symbol of ＇first generation＇, cf. [1]. The novelty here is the edge symbol σ∧ of ＇second generation＇, parametrised by （z, ζ） ∈ T＊Z ／ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.展开更多
文摘Amulti-dimensionally upwind conservative ResidualDistribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the case of the complex flowfield over a double cone configuration.The resulting numerical discretization combines a state-of-the-art nonlinear quasi-monotone second order blended scheme for distributing the convective residual and a standard Galerkin formulation for the diffusive residual.The physical source terms are upwinded together with the convective fluxes.Numerical results show an excellent agreement with experimental measurements and available literature.
基金supported by the National Natural Science Foundation of China(Grant Nos.11602269,11972034,and 11802213)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB22040301)the Research Program of Beijing,China(Grant Nos.Z161100002616034 and Z171100000817010)
文摘We theoretically construct a rectangular phononic crystal(PC) structure surrounded by water with C2vsymmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms:the vertical type, in which the distance s between the center of the scatterer and its right-angle point is greater than 0.5 a,and the transverse type, in which s is smaller than 0.5 a(where a is the crystal constant in the x direction). Each rectangular scatterer has three variables: length L, width D, and rotation angle θ around its centroid. We find that, when L and D change and θ is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary θ and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.
文摘In order to investigate the damage characteristic of ceramic-metal interpenetrating phase composite（IPC） under dynamic loading, uniaxial dynamic compression was performed to characterize the failure of SiC/Al composite with 15% porosity using a modifi ed Split Hopkinson Pressure Bar（SHPB）. High speed photography was used to capture the failure procedure and set up the relationship between deformation and real stress. The deformation control technology was used to obtain collected samples in different deformations under dynamic loading. Micro CT technology was utilized to acquire real damage distribution of these specimens. Moreover, SEM was employed in comparing the damage characteristics in IPC. A summary of the available experimental results showed that IPC without lateral confi nement formed double cones. The different features compared with ceramic materials without restraint was shown to be the result of the lateral restraint effect provided by metal phase to ceramics skeleton.
基金Supported by National Science Foundation of China(Grant No.11326073)Fundamental Research Funds for the Central Universities(Grant Nos.XDJK2013C134,SWU113061)Natural Scinece Foundation Project of CQ CSTC(Grant No.cstc 2014jcyjA00019)
文摘Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative answer to the question of Zhang.
文摘The variable high-order multiblock overlapping(overset)grids method of Sj¨ogreen&Yee[CiCP,Vol.5,2009]for a perfect gas has been extended to nonequilibrium flows.This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts[Wang et al.,J.Comput.Phys.,2009,2010]that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations.Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields,even under the multiblock grid or adaptive grid refinement framework.While low dissipative sixth-or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets,second-and thirdorder shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence.It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow for an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow.In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries.The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks,including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components,depending on the flow conditions.
基金The project is supported by the National Natural Science Foundation of China(19871005)the Scientific Research Foundation of the Education Department of Hebei Province(2001111).
文摘We consider the boundary value problem for the second order quasilinear differential equationwhere f is allowed to change sign, φ(v) = \v\p-2v, p > 1. Using a new fixed point theorem in double cones, we show the existence of at least two positive solutions of the boundary value problem.
文摘We study （pseudo-）differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are corner degenerate in a specific way. They are described Cmodulo ＇lower order terms＇） by a principal symbolic hierarchy σ（A） = （σψ （A）, σ∧ CA）, σ∧ （A））, where σψ is the interior symbol and σ∧（A） （y, η）, （y, η） ∈ T＊Y／0, the Coperator-valued） edge symbol of ＇first generation＇, cf. [1]. The novelty here is the edge symbol σ∧ of ＇second generation＇, parametrised by （z, ζ） ∈ T＊Z ／ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.
